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Stability of the Controller

I'm designing a smith predictor, as a part of the design I want to display the stability margins for the controller and plant, in my VI I tried to display the stability of the plant it looks like it is not working as it should be.For example I've identified that the stability of the plant when Kc of the PID controller is at 17.5, while running if I change the value of Kc to 50 then the stability changes to 'unstable" after some time if I put back the Kc to 17.5 the stability is still showing as unstable. However the graph is chnaging immeditely.I need some experts to help on this. VI attached here.

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Hello RKN,

I am trying to reproduce the issue but the VI is missing the PID Controller. Could you please include any dependencies so that I may be able to try and replicate the problem?

 

Wear
National Instruments
Product Support Engineer
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I've not opened your VI, but do remember that stability margins are (usually) defined on the basis of an open loop transfer function to show how stable or unstable the corresponding closed loop system will be. If is a common mistake to used the closed loop transfer function when calculating stability margins.

 

With a Smith Predictor strategy you have the added problem that you could look at the stability of the controller + real plant, or the stability of the controller + plant model with or without plant time delay depending where you take the transfer function from.

 

Also, make sure you are putting the time delay in a format that the stability analysis can accept - sometimes you might need to use a Pade approximation.

 

Consultant Control Engineer
www-isc-ltd.com
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